On Tue, Sep 3, 2024 at 6:44 PM Alan Grayson <[email protected]> wrote:
* > I fail to see how your comments relate to the possibly ambiguous > concept of the latter. The metric tensor field seems ambiguously defined.* *A N dimensional space is composed of an uncountable number of real numbers but it can be unambiguously defined by just N countable rational numbers, you can pair them up one to one. This is possible because there is only a countably infinite number of COMPUTABLE real numbers, the same rank of infinity as the rational numbers. So you can in effect give a rational number name to every real number you are able to find on the number line. You can do this even for a number such as π which is not only irrational, it's transcendental, because it is also computable. You can use an infinite series to get arbitrarily close to π. * *The vast majority of numbers on the number line are NOT computable (and have no name) but that's not really a problem despite the fact that the vast majority of numbers on the number line are NOT computable because, except for Chaitin's Omega Number, every number that a mathematician has ever heard of is a computable number. Computable numbers can have names, uncomputable numbers can not.* John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> und -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv13yFrwMMLBu7og_E%2BDVv9ab%3DTTJaB2wY%2B4kekuFJ6VuQ%40mail.gmail.com.
